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Joined 2026-09-21 Message
Incoming links: A. J. Cole
Publisher record and original extract: www.cambridge.org/core/journals/mathematical-gazette/article/abs/game-based-on-the-euclidean-algorithm-and-a-winning-strategy-for-it/99A7D31D926AF615AEB88F71CFAA9BB6
Introduces Euclid game. The wiki specifies its own terminal convention explicitly rather than assuming that all variants agree.
A. J. Cole 2026-11-05
A. J. Cole and A. J. T. Davie introduced Euclid game in a 1969 paper. They explicitly designed it to illustrate an algorithm for a winning strategy, making a familiar arithmetic procedure into a problem of combinatorial game theory.[ref]
A Game Based on the Euclidean Algorithm and a Winning Strategy for It by A. J. Cole and A. J. T. Davie. Original byline and introductory extract
The Euclidean algorithm repeatedly subtracts multiples of the smaller integer from the larger. Allowing a player to choose the multiple creates branching choices: termination alone is no longer the main question, because the player also cares who makes the last legal move. The terminal convention must therefore accompany any strategy statement.
A. J. T. Davie 2026-11-05
A. J. T. Davie coauthored A Game Based on the Euclidean Algorithm and a Winning Strategy for It by A. J. Cole and A. J. T. Davie with A. J. Cole. The original publisher record verifies the initials and joint authorship.[ref]
A Game Based on the Euclidean Algorithm and a Winning Strategy for It by A. J. Cole and A. J. T. Davie. Original 1969 byline and introductory extract
Their Euclid game turns the Euclidean algorithm into a contest: a legal subtraction is chosen by a player, so computing a greatest common divisor becomes a question about winning positions. The example connects an arithmetic algorithm with a constructive winning strategy in combinatorial game theory.